We reformulate the Smets-Wouters (2007) framework by embedding the theory of unemployment proposed in Galí (2011b, 2011c). We estimate the resulting model using postwar US data, while treating the unemployment rate as an additional observable variable. Our approach overcomes the lack of identification of wage markup and labor supply shocks highlighted by Chari, Kehoe, and McGrattan (2008) in their criticism of New Keynesian models, and allows us to estimate a "correct" measure of the output gap. In addition, the estimated model can be used to analyze the sources of unemployment fluctuations.